Coupling error model of 3-DoF-compliant stage based on parallelogram mechanism

Compliant mechanisms are the state-of-the-art in precision Compliant Parallelogram Stage (CPS) due to their many beneficial features. However, the translational motion of CPS is accompanied by parasitic displacement and coupling error in these mechanisms. In this paper, the parasitic displacements are analysed by firstly applying the pseudo-rigid-body theory to One-Degree of Freedom (1-DoF) CPS. Then the theoretical model of the Coupling Error Transfer Matrix (CETM) is presented on a Three-Degree of Freedom (3-DoF) serial CPS. Moreover, the general forms of CETM are developed for the various configurations of 3-DoF-compliant mechanisms. In addition, the coupling error model is validated through experiment on a 1-DoF CPS. Meanwhile, the analytical results are validated with Finite Element Analysis (FEA) by comparing the parasitic displacements on each coordination axial direction. Compared with the analysis results between theoretical calculation and the FEA method, the maximum difference of the parasitic displacement is about 0.18 uμ and the relative error of about 6.22%. This result offers effective ways to calculate and compensate for the coupling errors and serves to facilitate further work regarding the precision analysis of compliant mechanisms.